A promised potential of spaceborne interferometric synthetic aperture radars (InSAR) is a capability for regularly monitoring ground deformation with millimeter accuracy, for timely forecasting of impending natural hazards such as landslides. The main limitation in InSAR being actually capable of unleashing this potential for hazard prediction is that key precursory ground displacements are, in the majority of cases, a very small subset of the entire big data set provided by the method over large regions. Consequently, pinpointing a single impending failure may become very difficult or impossible. We develop a data‐driven framework that can handle such imbalanced spatiotemporal data based on the concept of outlying aspects mining, to find a subset of features out of a collection of potential features, which best distinguishes the landslide source area from the others. We show that the identified feature subspace can be used to find anomalous areas across multiple spatial scales, such that Sentinel‐1 satellite monitoring points which persistently lie in these areas can accurately detect the location of the Xinmo landslide (China) almost 1 year in advance—without false alarms. In a second case study, we identify the area affected by rockfalls on Stromboli volcano, a task that is generally infeasible with traditional methods applied to InSAR data. With continuing improvements in the spatial and temporal resolution from the new generation of satellites, such as Sentinel‐1, this approach opens the door to reliable and early prediction of failure over a broad range of slope instabilities.